Section 3.3.10.3.3. Non-pyroelectric acentric crystals

Finally, it is pointed out that electrical constraints of twin boundaries do not occur for non-pyroelectric acentric crystals. This is due to the absence of spontaneous polarization and, consequently, of electrical boundary charges. This fact is apparent for the Dauphiné and Brazil twins of quartz: they exhibit boundaries normal to the polar twofold axes which are reversed by the twin operations.

Nevertheless, it seems that among possible twin laws those leading to opposite directions of the polar axes are avoided. This can be explained for spinel twins of cubic crystals with the sphalerite structure and eigensymmetry . Two twin laws, different due to the lack of the symmetry centre, are possible:

In the first case, the sense of the polar axis [111] is not reversed, in the second case it is reversed. All publications on this kind of twinning, common in III–V and II–VI compound semiconductors (GaAs, InP, ZnS, CdTe etc.), report the twofold axis along [111] as the true twin element, not the mirror plane (111); this was discussed very early on in a significant paper by Aminoff & Broomé (1931).